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   "execution_count": 5,
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    {
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   "source": [
    "#format the book\n",
    "%matplotlib inline\n",
    "import book_format\n",
    "book_format.load_style(name='/custom3.css')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "input_collapsed": false
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   "source": [
    "# Nonlinear Filtering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Problem with Nonlinearity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* All of the equations of the classic Kalman filter are linear, so the filter can only handle linear problems. \n",
    "\n",
    "![](spring_m.jpg \"Weit on Spring\")\n",
    "\n",
    "* Suppose we wanted to track the motion of a weight on a spring where $F=0$. The equation for the motion with $m$ being the mass, $k$ the spring constant, and $c$ the damping force is \n",
    "\n",
    "$$m\\frac{d^2x}{dt^2} + c\\frac{dx}{dt} +kx = 0$$,\n",
    "\n",
    "which is a second order differential equation. It is not possible to write a linear equation for this equation, and therefore we cannot even formulate a design for the Kalman filter. \n",
    "\n",
    "* It is almost true to state that the only equation the entire mathematical community know how to solve is $\\mathbf{Ax}=\\mathbf{b}$. \n",
    "\n",
    "* One of solutions: linearize the problem, turning it into a set of linear equations.\n",
    "    * It's an approximation, so the answers are approximate. \n",
    "    * Linearizing a nonlinear problem gives inexact answers, and in a recursive algorithm like a Kalman filter tracking system these small errors can sometimes reinforce each other at each step, quickly causing the algorithm to spit out nonsense. \n",
    "    * There is not one obvious, correct, mathematically optimal solution anymore. We will forever be battling filters that *diverge*, that is, filters whose numerical errors overwhelm the solution. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## An Intuitive Look at the Problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Consider a tracking problem where we get the **range** and **bearing** to a target, and we want to track its position.\n",
    "* Suppose the distance is 50km, and the reported angle is 90$^\\circ$. \n",
    "* Assume that the errors in both range and angle are distributed in a Gaussian manner. \n",
    "    * Each time we take a reading the range will be $50\\pm\\sigma_{range}$ and the angle will be $90\\pm\\sigma_{angle}$. \n",
    "* What is the expected value of the position?\n",
    "    * Intuition: since the mean of the range will be 50km, and the mean of the angle will be 90$^\\circ$, so the answer will be x=0 km, y=90 km.\n",
    "* Varify the intuition\n",
    "    * Here are 300 points with a normal distribution of the distance of 0.4 km, and the angle having a normal distribution of 0.35 radians. \n",
    "    * Compute the average of the all of the positions, and display it as a star. Our intuition is displayed with a triangle."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
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eD4SHm7z9tp+wsEtXvPD7VTyehBzrTrdv340vvqhCly7BREcL7rnHSePGmfnk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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xafd69c2c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from numpy.random import randn\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "\n",
    "xs, ys = [], []\n",
    "N = 300\n",
    "for i in range (N):\n",
    "    a = math.pi / 2. + (randn() * 0.35)\n",
    "    r = 50.0         + (randn() * 0.4)\n",
    "    xs.append(r*math.cos(a))\n",
    "    ys.append(r*math.sin(a))\n",
    "\n",
    "plt.scatter(xs, ys, label='Measurements')\n",
    "plt.scatter(sum(xs)/N, sum(ys)/N, c='r', marker='*', s=200, label='Mean')\n",
    "plt.scatter(0, 50, c='k', marker='v', s=400, label='Intuition')\n",
    "plt.axis('equal')\n",
    "plt.legend(scatterpoints=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* We can see that the intuition failed us\n",
    "    * The nonlinearity of the problem forced all of the errors to be biased in one direction. This bias, over many iterations, can cause the Kalman filter to diverge."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Effect of Nonlinear Functions on Gaussians"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The mathematics of the Kalman filter is beautiful in part due to the Gaussian equation being so special. \n",
    "    * When we add and multiply it using linear algebra we get another Gaussian equation\n",
    "* At time $k$, the Kalman Filter passes the covariances through the process function to get the new covariance. The process function is linear, so the output is always another Gaussian.  \n",
    "    * Example: Pass an arbitrary Gaussian through the function $f(x) = 2x + 1$ and plot the result. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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V2tpaGjOwjUbqD/ShUKg0BgDG0tw0y+4SAACouIpvnBQOh3X+/HktWLBAkrRy5Uo1NDTo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\nqlyDaeHZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe2adbf6cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from numpy.random import normal\n",
    "\n",
    "data = normal(loc=0.0, scale=1, size=500000)\n",
    "ys = 2*data + 1\n",
    "\n",
    "plt.hist(ys,1000)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is an unsurprising result. The result of passing the Gaussian through $f(x)=2x+1$ is another Gaussian centered around 1. Let's look at the input, transfer function, and output at once."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "input_collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PXe8rh2DSmJlcZZwumORjzC8ngiBApwmDThOGlLgODW4jiiJqzAaUGYpwtqqo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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe2adbf6320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "def plot_transfer_func(data, f, lims, num_bins=1000):\n",
    "    ys = f(data)\n",
    "        \n",
    "    h = np.histogram(ys, num_bins, density=False)\n",
    "   \n",
    "    #plot output\n",
    "    plt.subplot(2,2,1)\n",
    "    plt.plot(h[0], h[1][1:], lw=4)\n",
    "    plt.ylim(lims)\n",
    "    plt.gca().xaxis.set_ticklabels([])\n",
    "    plt.title('output')\n",
    "\n",
    "    plt.axhline(np.mean(ys), ls='--', lw=2)\n",
    "\n",
    "    # plot transfer function\n",
    "    plt.subplot(2,2,2)\n",
    "    x = np.arange(lims[0], lims[1],0.1)\n",
    "    y = f(x)\n",
    "    plt.plot (x,y)\n",
    "    isct = f(0)\n",
    "    plt.plot([0,0,lims[0]],[lims[0],isct,isct],c='r')\n",
    "    plt.xlim(lims)\n",
    "    plt.ylim(lims)\n",
    "    plt.title('transfer function')\n",
    "\n",
    "    # plot input\n",
    "    h = np.histogram(data, num_bins, density=True)\n",
    "\n",
    "    plt.subplot(2,2,4)\n",
    "    plt.plot(h[1][1:], h[0], lw=4)\n",
    "    plt.xlim(lims)\n",
    "    plt.gca().yaxis.set_ticklabels([])\n",
    "    plt.title('input')\n",
    "\n",
    "    plt.show()\n",
    "\n",
    "def g(x):\n",
    "    return 2*x+1\n",
    "\n",
    "plot_transfer_func (data, g, lims=(-10,10), num_bins=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The plot labeled 'input' is the histogram of the original data. \n",
    "* The histogram is passed through the transfer function $f(x)=2x+1$ which is displayed in the chart to the upper right.\n",
    "    * The red lines shows how one value, $x=0$ is passed through the function. \n",
    "* Each value from input is passed through in the same way to the output function on the left.\n",
    "* For the output take the average of all the points, and draw the results with the dotted blue line. \n",
    "* The output looks like a Gaussian, and is in fact a Gaussian. \n",
    "    * The variance in the output is larger than the variance in the input, and the mean has been shifted from 0 to 1, which is what we would expect given the transfer function $f(x)=2x+1$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "* Unfortunately Gaussians are not closed under an arbitrary nonlinear function. \n",
    "    * Now let's look at a nonlinear function $f(x)=cos(4(x/2+0.7))-1.3x$,  and see how it affects the probability distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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XLlyIr776Crt375Y1uK2hEg3vkpiae85MmRERkSlMad/JugiCgOFhd6GHR5gs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\nIqJmYlNNRERERNRMbKqJiIiIiJrp/wFlV4CYBrFd9QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb03b0b8c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from numpy.random import normal\n",
    "import numpy as np\n",
    "\n",
    "data = normal(loc=0.0, scale=1, size=500000)\n",
    "\n",
    "def g(x):\n",
    "    return (np.cos(4*(x/2+0.7)))-1.3*x\n",
    "\n",
    "plot_transfer_func (data, g, lims=(-3.5,3.5), num_bins=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another nonlinear function  $f(x)=cos(4(x/2+0.7))sin(0.3x)-1.6x$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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D4yPnYMzQ6TR1hJAuiBJsctdEQgl83APg4x7Qalu9QQ+1RnEn+TY+r0vCb+Rk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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe2ad73e358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def g(x):\n",
    "    return (np.cos(4*(x/2+0.7)))*np.sin(0.3*x)-1.6*x\n",
    "\n",
    "plot_transfer_func (data, g, lims=(-3,3), num_bins=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The transfer function looks \"fairly\" linear - it is pretty close to a straight line, but the probability distribution of the output is completely different from a Gaussian.  \n",
    "\n",
    "* All of the equations of the Kalman filter assume that a Gaussian passed through the process function results in another Gaussian. If this is not true then all of the assumptions and guarantees of the Kalman filter do not hold. \n",
    "\n",
    "Let's look at what happens when we pass the output back through the function again, simulating the next step of the Kalman filter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PzL7Ba1Y34sCFL3A6+QDmTXgQk8fMhdBOZJtgCSHd6tNp+gixFj7fDm4KL4sr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\nExERERGZ0P8HRLz1p4rtToMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe2adbf6780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y=g(data)\n",
    "plot_transfer_func (y, g, lims=(-3,3), num_bins=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The probability function is further distorted from the original Gaussian. \n",
    "* However, the graph is still somewhat symmetric around x=0, let's see what the mean is."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "input  mean, variance: -0.0017, 0.9984\n",
      "output mean, variance: -0.0251, 2.2377\n"
     ]
    }
   ],
   "source": [
    "print ('input  mean, variance: %.4f, %.4f'% (np.average(data), np.std(data)**2))\n",
    "print ('output mean, variance: %.4f, %.4f'% (np.average(y), np.std(y)**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare that to the linear function that passes through (-2,3) and (2,-3), which is very close to the nonlinear function we have plotted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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kWLczDAdSsQJysSsUEg94ufrB29UfXq494Knwg7MTv/1eLCHEYVF+dzxSsRwL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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe2ac953400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "output mean, variance: 0.0025, 2.2465\n"
     ]
    }
   ],
   "source": [
    "def h(x): return -1.5*x\n",
    "plot_transfer_func (data, h, lims=(-4,4), num_bins=300)\n",
    "out = h(data)\n",
    "print ('output mean, variance: %.4f, %.4f'% (np.average(out), np.std(out)**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Although the shapes of the output are very different, the mean and variance of each are similar.\n",
    "* This may lead us to reasoning that perhaps we can ignore this problem if the nonlinear equation is 'close to' linear.\n",
    "* To test that, we can iterate several times and then compare the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "linear    output mean, variance: 0.1464, 7470.2300\n",
      "nonlinear output mean, variance: -1.5418, 26163.4005\n"
     ]
    }
   ],
   "source": [
    "out = h(data)\n",
    "out2 = g(data)\n",
    "\n",
    "for i in range(10):\n",
    "    out = h(out)\n",
    "    out2 = g(out2)\n",
    "print ('linear    output mean, variance: %.4f, %.4f' % \n",
    "       (np.average(out), np.std(out)**2))\n",
    "print ('nonlinear output mean, variance: %.4f, %.4f' % \n",
    "       (np.average(out2), np.std(out2)**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Unfortunately the nonlinear version is not stable. \n",
    "    * It drifts significantly from the mean of 0, and the variance is half an order of magnitude larger. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A 2D Example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Think about tracking an aircraft with radar, which may have a covariance that looks like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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guSG2ew56joOu14UVWTDUMk4vcEY3Ec2fOMmw1fGQxRWcME5hqa5jo22gVOL9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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe2ad6869e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import stats\n",
    "import numpy as np\n",
    "P = np.array([[6, 2.5], [2.5, .6]])\n",
    "stats.plot_covariance_ellipse((10, 2), P,  facecolor='g', alpha=0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So what happens when we try to linearize this problem?\n",
    "* The radar gives a range to the aircraft. \n",
    "* Suppose the radar is directly under the aircraft (x=10) and the next measurement states that the aircraft is 3 miles away (y=3). \n",
    "    * The positions that could match that measurement form a circle with radius 3 miles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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dxWJhfnuQ+e1BDvZn+eOmfl7dkzimVWEqq/Gbpw/yxAu9XLGygSsuaMDnkTgx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\nEc0Shm8iIiIiolnyfwHRFOvK5TfwawAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe2ac334080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.patches import Ellipse\n",
    "circle1=plt.Circle((10,0),3,color='#004080',fill=False,linewidth=4, alpha=.7)\n",
    "ax = plt.gca()\n",
    "ax.add_artist(circle1)\n",
    "plt.xlim(0,10)\n",
    "plt.ylim(0,3)\n",
    "\n",
    "stats.plot_covariance_ellipse((10, 2), P,  facecolor='g', alpha=0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The probable position of the aircraft is somewhere near x=11.4, y=2.7 because that is where the covariance ellipse and range measurement overlap. \n",
    "* But the range measurement is nonlinear so we have to linearize it.\n",
    "    * Linearize at the last position of the aircraft - (10,2). \n",
    "    * At x=10 the range measurement has y=3, and so we linearize at that point."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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CeUc4ic5wcsyPeSkEcl03cmE7k0VSlJEWZaSVXNBOyxlkdQkOmwluhwWVgVx/7cFyo94u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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe2ad7c7b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.patches import Ellipse\n",
    "circle1=plt.Circle((10,0),3,color='#004080',fill=False,linewidth=4, alpha=.7)\n",
    "ax = plt.gca()\n",
    "ax.add_artist(circle1)\n",
    "plt.xlim(0,10)\n",
    "plt.ylim(0,3)\n",
    "plt.axhline(3, ls='--')\n",
    "stats.plot_covariance_ellipse((10, 2), P,  facecolor='g', alpha=0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Now we have a linear representation of the problem (literally a straight line) which we can solve.\n",
    "* Unfortunately you can see that the intersection of the line and the covariance ellipse is a long way from the actual aircraft position."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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LlqB1dmI5zY4nWmcnliVLZnlUM8vttGKz54llEwwnfdQGPZUe0pxx0pnv2SQz3/PHfJ4t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\ndQQi8Yzxv79+Nc5fxr6umZJlGQOjYfQMBzEYHsZ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CBwx6vlFMdCpOfvjOHuWKyjJ8NZkl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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe2ad802b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.patches import Ellipse\n",
    "circle1=plt.Circle((10,0),3,color='#004080',fill=False,linewidth=4, alpha=.7)\n",
    "ax = plt.gca()\n",
    "ax.add_artist(circle1)\n",
    "plt.xlim(0,10)\n",
    "plt.ylim(0,3)\n",
    "plt.axhline(3, ls='--')\n",
    "stats.plot_covariance_ellipse((10, 2), P,  facecolor='g', alpha=0.2)\n",
    "plt.scatter([11.4], [2.65],s=200)\n",
    "plt.scatter([12],[3], c='r', s=200)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* That sort of error often leads to disastrous results.\n",
    "    * In the next innovation of the filter that very bad estimate will be used to linearize the next radar measurement, so the next estimate is likely to be markedly worse than this one. \n",
    "    * After only a few iterations the Kalman filter will diverge, and start producing results that have no correspondence to reality.\n",
    "* You will always be battling divergence when working with nonlinear systems."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
